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# India's Bathroom Tiles

Alignments to Content Standards: 3.MD.C.7.a

India is remodeling her bathroom.  She plans to cover the bathroom floor with tiles that are each 1 square foot.  Her bathroom is 5 feet wide and 8 feet long.  India needs to stay within a strict budget and must purchase the exact number of tiles needed.

## IM Commentary

This task allows students to use the concept of "tiling" as an entry point to linking area with multiplication.  Ideally, they would be given foam or plastic tiles to actually practice putting the tiles on the space without gaps or overlaps.

Students may find the total number of tiles needed by counting all, using repeated addition or using multiplication.  For the students who do not see the immediate relationship between area and multiplication, it might be helpful to have students explain their reasoning.  One student might reason that there are 8 rows of 5 tiles, so there are 8 x 5 or 40 tiles.  Another student might reason that there are 5 columns of 8 tiles each, so there are 5 x 8 or 40 tiles.

Teachers will also have to help students understand that they are finding the number of tiles that India needs to remodel the bathroom, but that each tile represents one square foot.  We find the number of tiles needed by finding the number of square feet we need to cover.

## Solution

India will need to buy 40 tiles because she has 40 square feet of bathroom floor to cover.  We can see this as 8 rows with 5 tiles in each row or 5 columns with 8 tiles in each column, so we can find the total number of tiles by multiplying: 8 x 5 = 40. We can illustrate this with a picture as well.

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#### Kristin says:

Dear Math professor and curriculum writer,

Thank you for your comment. This is not meant to be a modeling problem, but a thought experiment to help students see the connection between multiplication and area. Before students can apply mathematics to a real-world context, they have to make some more fundamental connections between mathematical concepts (such as multiplication) and the kinds of contexts in which such a concept should legitimately apply (such as areas of rectangles, equal groups, multiplicative comparison scenarios, and so on). Note that this is a task for third-graders who are unlikely to have ever purchased tiles for a flooring project, so their experiences of the real world are unlikely to interfere with the thought experiment that the task is trying to establish. We have other tasks meant to illustrate the practice of modeling mathematics, although we wish we had more (good modeling tasks are well-crafted and time-intensive to develop).

Your criticisms of the task as modeling problem are well taken, and if we had meant it to be such a task, we would make appropriate changes based on your feedback. Clearly the purpose of this task was not well-stated for you to have thought it was meant as a modeling item. We welcome suggestions for clarifying the commentary so the real purpose of the task is made clear.

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